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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.2//EN"><!--Converted with LaTeX2HTML 96.1-h (September 30, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --><HTML><HEAD><TITLE>Recurrence plots</TITLE><META NAME="description" CONTENT="Recurrence plots"><META NAME="keywords" CONTENT="TiseanHTML"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><LINK REL=STYLESHEET HREF="TiseanHTML.css"></HEAD><BODY bgcolor=ffffff LANG="EN" > <A NAME="tex2html212" HREF="node15.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html210" HREF="node13.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html204" HREF="node13.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html213" HREF="node15.html">Space-time separation plot</A><B>Up:</B> <A NAME="tex2html211" HREF="node13.html">Visualizationnon-stationarity</A><B> Previous:</B> <A NAME="tex2html205" HREF="node13.html">Visualizationnon-stationarity</A><BR> <P><H2><A NAME="SECTION00041000000000000000">Recurrence plots</A></H2><P>Recurrence plots are a useful tool to identify structure in a data set in atime resolved way qualitatively. This can be intermittency (which one detectsalso by direct inspection), the temporary vicinity of a chaotic trajectory toan unstable periodic orbit, or non-stationarity. They were introducedin [<A HREF="citation.html#Ruelle">37</A>] and investigated in much detail in [<A HREF="citation.html#Casdagli_recurr">38</A>],where you find many hints on how to interprete the results. Our routine<a href="../docs_c/recurr.html">recurr</a> simply scans the time series and marks each pair of time indices(<I>i</I>,<I>j</I>) with a black dot, whose corresponding pair of delay vectors hasdistance <IMG WIDTH=22 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline6759" SRC="img42.gif">. Thus in the (<I>i</I>,<I>j</I>)-plane, black dots indicatecloseness. In an ergodic situation, the dots should cover the plane uniformlyon average, whereas non-stationarity expresses itself by an overall tendencyof the dots to be close to the diagonal. Of course, a return to a dynamicalsituation the system was in before becomes evident by a black region far awayfrom the diagonal. In Fig. <A HREF="node14.html#figvisualrecur"><IMG ALIGN=BOTTOM ALT="gif" SRC="icons/cross_ref_motif.gif"></A>, a recurrence plot is usedto detect transient behavior at the beginning of a longer recording.<P><P><blockquote><A NAME="4671"> </A><IMG WIDTH=328 HEIGHT=319 ALIGN=BOTTOM ALT="figure568" SRC="img43.gif"><BR><STRONG>Figure:</STRONG> <A NAME="figvisualrecur"> </A> Recurrence plot for Poincaré section data from a vibrating string experiment [<A HREF="citation.html#string">39</A>]. Above the diagonal an embedding in two dimensions was used while below the diagonal, scalar time series values were compared. In both cases the lighter shaded region at the beginning of the recording indicates that these data are dynamically distinct from the rest. In this particular case this was due to adjustments in the measurement apparatus.<BR></blockquote><P><P>For the purpose of stationary testing, the recurrence plot is not particularlysensitive to the choice of embedding. The contrast of the resulting images canbe selected by the distance <IMG WIDTH=6 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline6495" SRC="img3.gif"> and the percentage of dots that shouldbe actually plotted. Various software involving the color rendering andquantification of recurrence plots is offered in DOS executable form byWebber [<A HREF="citation.html#webber">40</A>]. The interpretation of the often intriguing patternsbeyond the detection and study of non-stationarity is still an open question.For suggestions for the study of nonstationary signals see [<A HREF="citation.html#habil">3</A>] andreferences given there.<P><HR><A NAME="tex2html212" HREF="node15.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html210" HREF="node13.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html204" HREF="node13.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html213" HREF="node15.html">Space-time separation plot</A><B>Up:</B> <A NAME="tex2html211" HREF="node13.html">Visualizationnon-stationarity</A><B> Previous:</B> <A NAME="tex2html205" HREF="node13.html">Visualizationnon-stationarity</A><P><ADDRESS><I>Thomas Schreiber <BR>Wed Jan 6 15:38:27 CET 1999</I></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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